{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Loading Hyperbolic Orbits into REBOUND\n",
    "\n",
    "Imagine we have a table of orbital elements for comets (kindly provided by Toni Engelhardt)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from io import StringIO\n",
    "import numpy as np\n",
    "import rebound\n",
    "epoch_of_elements = 53371.0 # [MJD, days]\n",
    "c = StringIO(u\"\"\"\n",
    "# id     e          q[AU]      i[deg]      Omega[deg]  argperi[deg]  t_peri[MJD, days]  epoch_of_observation[MJD, days]\n",
    "168026   12.181214  15.346358  136.782470  37.581438   268.412314    54776.806093       55516.41727\n",
    "21170    2.662235   2.013923   140.646538  23.029490   46.292039     54336.126288       53673.44043   \n",
    "189298   15.503013  11.550314  20.042232   203.240743  150.855761    55761.641176       55718.447145 \n",
    "72278    34.638392  24.742323  157.984412  126.431540  178.612758    54382.158401       54347.240445\n",
    "109766   8.832472   9.900228   144.857801  243.102255  271.345342    55627.501618       54748.37722\n",
    "\"\"\")\n",
    "comets = np.loadtxt(c) # load the table into a numpy array"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We  want to add these comets to a REBOUND simulation(s).  The first thing to do is set the units, which have to be consistent throughout.  Here we have a table in AU and days, so we'll use the gaussian gravitational constant (AU, days, solar masses).  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "sim = rebound.Simulation()\n",
    "k = 0.01720209895 # Gaussian constant\n",
    "sim.G = k**2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We also set the simulation time to the epoch at which the elements are valid:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "sim.t = epoch_of_elements"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We then add the giant planets in our Solar System to the simulation.  You could for example query JPL HORIZONS for the states of the planets at each comet's corresponding epoch of observation (see [Horizons.ipynb](../Horizons)).  Here we set up toy masses and orbits for Jupiter & Saturn:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "sim.add(m=1.) # Sun\n",
    "sim.add(m=1.e-3, a=5.) # Jupiter\n",
    "sim.add(m=3.e-4, a=10.) # Saturn"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "Let's write a function that takes a comet from the table and adds it to our simulation:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def addOrbit(sim, comet_elem):\n",
    "    tracklet_id, e, q, inc, Omega, argperi, t_peri, epoch_of_observation = comet_elem\n",
    "    sim.add(primary=sim.particles[0], \n",
    "            a = q/(1.-e),\n",
    "            e = e,\n",
    "            inc = inc*np.pi/180.,  # have to convert to radians\n",
    "            Omega = Omega*np.pi/180.,\n",
    "            omega = argperi*np.pi/180.,\n",
    "            T = t_peri  # time of pericenter passage\n",
    "           )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "By default, REBOUND adds and outputs particles in Jacobi orbital elements.  Typically, orbital elements for comets are heliocentric.  Mixing the two will give you relative errors in elements, positions etc. of order the mass ratio of Jupiter to the Sun ($\\sim 0.001$) which is why we pass the additional `primary=sim.particles[0]` argument to the `add()` function.  If this level of accuracy doesn't matter to you, you can ignore the `primary` argument.\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can now set up the first comet and quickly plot to see what the system looks like:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 500x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "addOrbit(sim, comets[0])\n",
    "%matplotlib inline\n",
    "op = rebound.OrbitPlot(sim,xlim=[-20.,20],ylim=[-20.,20])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we just integrate until whatever final time we’re interested in.  Here it's the epoch at which we observe the comet, which is the last column in our table:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 500x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "tfinal = comets[0][-1]\n",
    "sim.integrate(tfinal)\n",
    "op = rebound.OrbitPlot(sim,xlim=[-20.,20],ylim=[-20.,20])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "REBOUND automatically find out if you want to integrate forward or backward in time."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For fun, let's add all the comets to a simulation:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 500x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sim = rebound.Simulation()\n",
    "sim.G = k**2\n",
    "sim.t = epoch_of_elements \n",
    "sim.add(m=1.) # Sun\n",
    "sim.add(m=1.e-3, a=5.) # Jupiter\n",
    "sim.add(m=3.e-4, a=10.) # Saturn\n",
    "for comet in comets:\n",
    "    addOrbit(sim, comet)\n",
    "op = rebound.OrbitPlot(sim,xlim=[-50.,50],ylim=[-50.,50])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}
